Nonlinear Morphoelastic Plates I: Genesis of Residual Stress

Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate is given. Balance equations are derived via the global constraint principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed and the existence of residually stressed states is established

Nonlinear morphoelastic plates II: exodus to buckled states

Morphoelasticity is the theory of growing elastic materials. This theory is based on the multiple decomposition of the deformation gradient and provides a formulation of the deformation and stresses induced by growth. Following a companion paper, a general theory of growing nonlinear elastic Kirchhoff plate is described. First, a complete geometric description of incompatibility with simple examples is given. Second, the stability of growing Kirchhoff plates is analyzed

Design of an integrated shallow water wave experiment

The experimental design and instrumentation for an integrated shallow-water surface gravity wave experiment is discussed. The experiment required the measurement of the water surface elevation, meteorological parameters, and directional spectra at a number of locations on a shallow lake. In addition, to acquire data under a wide range of conditions, an experimental period of three years was required. A system of telephone and radio modem links were installed to enable real-time monitoring of instrument performance at eight separate measurement locations on the lake. This system also enabled logging sessions to be optimized to ensure the maximum possible data return from this extended experimentIEEE Oceanic Engineering Societ

VLA neutral hydrogen imaging of compact groups

Images of the neutral hydrogen (H I) in the direction of the compact groups of galaxies, HCG 31, HCG 44, and HCG 79 are presented. The authors find in HCG 31 and HCG 79, emission contained within a cloud much larger than the galaxies as well as the entire group. The H I emission associated with HCG 44 is located within the individual galaxies but shows definite signs of tidal interactions. The authors imaged the distribution and kinematics of neutral hydrogen at the two extremes of group sizes represented in Hickson's sample. HCG 44 is at the upper limit while HCG 18, HCG 31, and HCG 79 are at the lower end. Although the number of groups that have been imaged is still very small, there may be a pattern emerging which describes the H I morphology of compact groups. The true nature of compact groups has been the subject of considerable debate and controversy. The most recent observational and theoretical evidence strongly suggests that compact groups are physically dense, dynamical systems that are in the process of merging into a single object (Williams and Rood 1987, Hickson and Rood 1988, Barnes 1989). The neutral hydrogen deficiency observed by Williams and Rood (1987) is consistent with a model in which frequent galactic collisions and interactions have heated some of the gas during the short lifetime of the group. The H I disks which are normally more extended than the luminous ones are expected to be more sensitive to collisions and to trace the galaxy's response to recent interactions. Very Large Array observations can provide in most cases the spatial resolution needed to confirm the dynamical interactions in these systems

Dorsalization of the neural tube by the non-neural ectoderm

The patterning of cell types along the dorsoventral axis of the spinal cord requires a complex set of inductive signals. While the chordamesoderm is a well-known source of ventralizing signals, relatively little is known about the cues that induce dorsal cell types, including neural crest. Here, we demonstrate that juxtaposition of the non-neural and neural ectoderm is sufficient to induce the expression of dorsal markers, Wnt-1, Wnt-3a and Slug, as well as the formation of neural crest cells. In addition, the competence of neural plate to express Wnt-1 and Wnt-3a appears to be stage dependent, occurring only when neural tissue is taken from stage 8–10 embryos but not from stage 4 embryos, regardless of the age of the non-neural ectoderm. In contrast to the induction of Wnt gene expression, neural crest cell formation and Slug expression can be induced when either stage 4 or stage 8–10 neural plates are placed in contact with the non-neural ectoderm. These data suggest that the non-neural ectoderm provides a signal (or signals) that specifies dorsal cell types within the neural tube, and that the response is dependent on the competence of the neural tissue